I was going to show off and say it is a mammilaria, but Hywel got there first. Yours could do with going into a bigger pot. Use special cactus compost, which you can buy in quite small bags. Wear a nice thick glove, tip the pot so the gloved hand supports the cactus and see if it drops out easily. If it doesn't you might be able to encourage it by sticking something up through the drainage hole. If all else fails you might need to cut the pot with a stanley knife. Choose a new pot at least an inch wider than the present one. You might like to top dress with grit to make sure that the plant is not in contact with damp soil. In winter you will only need to water it a little once a month. In mid spring you can give it a good watering, and it may then surprise you with some flowers. During hot weather you can water if more frequently but always err on the side of dryness rather than risk overwatering. Mammilarias thrive in full sun.

My first ever purchased plant was a cactus, it was my tenth birthday and also the first time I was allowed to go down town on my own, cost halfacrown from woolworths and was only as big as my thumb, sadly its gone now but I had it for over 40yrs.........

My first plant was a cactus too, an opuntia microdasys (if I have the spelling right after all these years!) I wanted it because there was a picture of one with a little black girl on some children's notepaper I was given. Little did the person who gave me the notepaper know what she was starting!